Knights always tell the truth and Knaves always lie. There was a second book about Humans and Vampires. Humans always tell the truth, vampires always lie, insane humans think they are telling the truth but lie, and insane vampires think they are lying but always tell the truth. Then there's a bunch of riddles of this sort.

Its faster to just check if a number, modulo 6469693230 has a prime remainder, since all prime numbers do.

03-27-2009

Tonto

Number theory in 21 minutes

The greatest common factor explanation of this is great

03-27-2009

Sebastiani

Number theory in 21 minutes

>> Its faster to just check if a number, modulo 6469693230 has a prime remainder, since all prime numbers do.

Are you sure about that? Can you elaborate?

03-27-2009

Snafuist

Riddle #3: three dwarfs, two paths, one life

Ok, just to bring this to an end:

First, you ask a random dwarf: "Who of your brothers lies more often?"

If you happen to ask A, he will correctly point to C.
If you happen to ask B, he will incorrectly point to C.
If you happen to ask C, he will randomly point to either A or B.

In either case, the dwarf not asked and not pointed to is not C.

Ask this dwarf the following question: "Which path would the dwarf suggest who is the exact opposite of you?"

If you ask A, he will tell the truth and provide you with the path that B would've suggested, i.e. the wrong path.
If you ask B, he will lie and provide you with the path that A would'nt have suggested, i.e. the wrong path.

So you take the other path.

Greets,
Philip

03-27-2009

laserlight

Riddle #3: three dwarfs, two paths, one life

hmm... but that seems to assume that the dwarves are benevolent. If they are (or more accurately, could be) malicious, then you have to phrase that second question more explicitly to your advantage.

03-27-2009

Snafuist

Riddle #5: more dwarfs

There are seven dwarfs, each one wearing a unique hat. A wind blows off the hats. The dwarfs start running after their hats and each dwarf puts on the first hat that he manages to catch. Eventually every dwarf has a hat again.

What is the probability that exactly six dwarfs are wearing their own hat now?

Greets,
Philip

03-27-2009

Snafuist

Riddle #3: three dwarfs, two paths, one life

Quote:

Originally Posted by laserlight

hmm... but that seems to assume that the dwarves are benevolent. If they are (or more accurately, could be) malicious, then you have to phrase that second question more explicitly to your advantage.

Right. I already had several discussions about that. The problem arises due to the inexactness of most natural languages. The most obvious solution is to ask a more concise (and more awful) question. Personally, I prefer adding the proposition to the riddle that the dwarfs are benevolent. I didn't do it in the first place because it only distracts from the intended solution, but it's good that you pointed it out.

Greets,
Philip

03-27-2009

laserlight

Riddle #3: three dwarfs, two paths, one life

Quote:

Originally Posted by Snafuist

The problem arises due to the inexactness of most natural languages.

I don't think so. I think that it is merely an unstated assumption. I wanted to propose the solution of just capturing the dwarves and dragging them in a direction to see their response, but then I realised that I could not be sure that the dwarves were not so bored with their existence that they intended suicide, hence I would have to ask them questions anyway :o